What is the scalar product of the vectors $a = 3\hat{i} - 4\hat{j} + 5\hat{k}$ and $b = -2\hat{i} +

Question

What is the scalar product of the vectors $a = 3\hat{i} - 4\hat{j} + 5\hat{k}$ and $b = -2\hat{i} + \hat{j} - 3\hat{k}$?

Professor PC Thomas Classes · Answer

The scalar (dot) product is given by $a \cdot b = (a_x)(b_x) + (a_y)(b_y) + (a_z)(b_z) = (3)(-2) + (-4)(1) + (5)(-3) = -6 - 4 - 15 = -25$.